Fuzzy Geodetic and Detour Spectra: Geodetic-Laplacian Energy in Fuzzy Graphs

Authors

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i4.6307

Keywords:

Fuzzy graphs, Geodetic spectrum, Detour spectrum, Geodetic-Laplacian energy

Abstract

This research study delves into the spectral characteristics and energy measures associated with fuzzy graphs. We present the fuzzy geodetic spectrum and fuzzy detour spectrum, which capture the spectral properties of fuzzy graphs under geodetic and detour constraints. In addition, we propose and derive novel expressions for the fuzzy geodetic-Laplacian and detour-Laplacian energies, incorporating both upper and lower bounds. Towards the end, a real-world application of fuzzy geodetic-Laplacian energy pertaining to illegal immigration and human trafficking is described. It emphasizes its potential to improve decision-making measures, allowing more effective and coordinated crime prevention and resolution initiatives.

Author Biographies

  • R. Rajeshkumar, Manonmaniam Sundaranar University, Tirunelveli

    Research Scholar, Department of Mathematics, Malankara Catholic College.

  • Anto A. M, St. Albert's College (Autonomous), Kochi, Kerala, India.

    Dr. Anto. A. M 

    Assistant Professor,

    A O Konnully Memorial Research Centre and Department of Mathematics 

    St. Albert's College(Autonomous), Kerala, India.

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Published

2025-11-05

Issue

Vol. 18 No. 4: (October 2025)

Section

Discrete Mathematics

License

Copyright (c) 2025 R. Rajeshkumar, Anto A. M, V. Mary Mettilda Rose

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How to Cite

Fuzzy Geodetic and Detour Spectra: Geodetic-Laplacian Energy in Fuzzy Graphs. (2025). European Journal of Pure and Applied Mathematics, 18(4), 6307. https://doi.org/10.29020/nybg.ejpam.v18i4.6307